Equations derived from Blake's (1952) model of diverging waves from a point source were programmed for computer analysis. Variations of the displacement resulting from changes in the pressure function, propagational velocity, range, and cavity size were investigated. Results of the research indicate that: (1) a step pressure function used with this model gives displacements that closely approximate the displacements measured at 0.4 km from the Gnome nuclear explosion; (2) near the source, long-period displacements are inherent with this model; (3) the periods of the maximum Fourier transform amplitude of the radiation field is proportional to the equivalent cavity radius; (4) the peak displacements scale to the two-thirds power of charge size for values of a between 80 (0.5 kt) and 600 m (275 kt); and (5) between 0.1 and 3.0 cps, the amplitudes of given frequencies scale to the first power of charge size for values of a between 145 (3 kt) and 305 m (28 kt). In general, Fourier amplitudes at frequencies below the natural frequency of the cavity scale to the first power of charge size, and Fourier amplitudes at frequencies above the natural frequency of the cavity scale to a fractional power of charge size. It is suggested that this may be a good model with which to compare near-source observations of seismic phenomena.